how I can make the mesh invisible and keep the fire?
If your mesh is one piece, and you don't want to work destructively,just go in the edit mode and select the unrequired vertices and hit H on keyboard to hide it
You can unhide it by alt+H
If your mesh in seperate,just click on eye button in the outlined
If you want your mesh to be seperate,select the unrequired vertices and press P to seperate it as other mesh